Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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Why Black Scholes model needs to assume S_t follows GBM if physical probabilities do not matter?

Beginner here learning about black scholes looking for a high level/intuitive explanation. So I've learned that the physical/"true" probabilities of S_t (or whatever underlying asset) do not ...
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2 votes
2 answers
162 views

Numeraire explanation on currency greeks

Would it be possible to help understand the numeraire of certain currency options? Derivations from the Black Scholes models for Delta and Gamma, $Delta = e^{-r_f T} N(d_1)$ $Gamma = \frac{e^{-r_f T}}{...
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probability of exercise

I am pricing a bermudan call option using finite difference method. At each exercise time on the grid I have points I exercise and on some of those I don't. Thus, at any given call time there is a ...
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Calendar arbitrage with dividends

In this question, it is shown: i) the definition of calendar arbitrage for Call options; ii) the financial/mathematical rationale. Nevertheless, in that question, one assumes that there are no ...
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2 votes
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Why do Futures Contracts use variation in the US, but options don’t?

Sorry if this is obvious, but I was reading up on Futures and the concept of variation margin intrigued me. Options settle like Stocks and have unrealized gain/loss without affect on cash flow during ...
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Is “at the money” referent to the spot or forward price?

This may be a trivial question, but one I wasn’t sure about. Imagine I want to buy a 1 year ATM straddle. Does “at the money” imply buying closest to the current spot price, or does it mean to buy at ...
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1 vote
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775 views

Effect of Implied volatility on option delta

I am currently hedging a short put option where strike is 6027 and expiry is 30th Mar 2023. As per my understanding when option is ITM increase in volatility will decrease the delta and decrease in ...
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Calculation of SABR delta

I have a relatively simple question on the calculation of the SABR delta. I consider the Bartlett's delta (although my question remains the same for the unadjusted SABR delta from Hagan (2002) ). The ...
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Is there some reason for volatility smile minima to be displaced from ATM?

I am analyzing some options data and I see that the volatility smile has its minima a few strikes higher than the current traded price (about 2.5 % higher than spot). I have checked my data thoroughly....
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Is this generalization of the Kelly Criterion valid and already known in the literature?

The classic case of a stock and bond Well known in the literature is the Kelly-Criterion in terms of Merton's portfolio problem with log-utility. To recall the specific framework, let $S_t$ be a ...
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Why does bull call spread shows higher payoff than bull put spread?

I am trying to compare bull call spread and bull put spread for equity index option. For the options where the put call parity holds, I am getting a different payoff for bull call spread and bull put ...
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Quantlib Black Model for Commodity Options (Interest Rate Options) is extremely light on gamma and price vs BBG, is model incorrect?

I am using the QuantLib developers example to try and price a TY option. The Delta is pretty close but the price and gamma are way off (almost by a factor of 2). Am I using the model wrong or is the ...
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Short gamma position when option is going toward ATM

Short gamma position when option is going toward ATM, does it better to close out the option in terms of PNL? or is there any other choices? (in case of Delta-hedging portfolio)
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Volatility targeting / sizing for option strategies

I am trying to work out how to properly size an option strategy to a given target volatility. Assuming I have \$100 capital and I would like to have a strategy's long-run daily volatility to be \$1 (e....
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Callable Corporate Bonds: Why Issue a Callable Bond That Has a First Call Date <6 months to Final Maturity?

My understanding is that firms typically issue callable bonds to benefit from possible refinancing in a lower interest rate environment. What, then, is the point of issuing a bond, say, today (06/30/...
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Long gamma + hard delta / Short gamma + soft delta

If my position is Long gamma and future volatility is rising, is hard delta (delta hedging using Futures) more profitable than soft delta? On the contrary, if my position is Short gamma and future ...
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-3 votes
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How do we analyse the future and option market on the base of the Fama-French model?

How do we analyse the future and option market on the base of the Fama-French model? Basically i want to know can we analyse derivative market on base of FAMA French or CAPM model ? e.g for stock we ...
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140 views

Best/worst case scenario after selling OTM call option

You decide to sell a European call option that is currently 10% OTM (for example the strike = 100 and the current price = 90). You have to delta hedge to keep the delta of your position at 0. What is ...
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Delta-Gamma VaR approximation and cross-gamma

Suppose we have a portfolio of say two vanilla options (e.g. on two index futures). One option A with underlying X and a second option B with underlying Y. I'm trying to calculate the delta-gamma ...
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About American Forward Pricing

I just want to know if there is an analytical solution about FX American forward. I recently get a solution that computes price for each τ-maturity forward contract and then take a maximum price. So, ...
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11 votes
1 answer
972 views

What's the most efficient way to store options and time series data for backtesting?

I would like to know what database would you guys use for storing around 500GB-1TB of options and time series tick data. The idea is to use it for backtesting so it would have to be as efficient as ...
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2 votes
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Do single name stock option volatility surfaces exhibit steeper volatility smiles after stock price crash episodes?

In index options, there was not much of a smile (on the put-side) until the 1987 market crash. I'm wondering if the same applies to single name stocks? That is, do price crashes in individual stocks ...
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2 votes
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Does time remaining matter in NO Touch-ONE Touch probabilities?

I asked a question some days back and got an answer which I understand and make sense: Probability of touching short call strike and not touching touching short put strike of a short strangle? However,...
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Vega Surface with Local Volatility Model

I am trying to obtain the Vega of some equities with the Dupire local volatility model. For this I have already validated the pricing model (I am using Monte Carlo) and now I am able to obtain the ...
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6 votes
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379 views

Black-Scholes: Volatility Smile "sharpens" with time to expiry

I have tried to calculate IV and log-moneyness (=log(S/K)) for different times to expiry (M = less than 1 month, Q = less than 1 quarter, S = less than 1/2 of an year, Y = less than 1 year, Y (+) = ...
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12 votes
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Mark Joshi's book - quant interview questions

I am currently doing the question on pricing the option with payoff: $$\max (S(S-K),0).$$ On the relevant question section, it's asked why would a bank be reluctant to sell such option? I can't really ...
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1 vote
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Sell weekly covered calls repeatly

If underlying stock prices are random walk in short term, then it doesn't matter where the price go. What we can definitely certain, is the high Theta in ATM options. Can we repeatedly sell weekly put,...
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Questions regarding a “lite/kindergarten” Barbell investement strategy implementation

The idea for this question is more or less taken from a slight hint regarding how Universa Investments L.P. functions from Taleb's Antifragile (obviously the real case is far more complex but this is ...
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Valuing a call option that is issued today, exercisable after 2 years from the issue date and expires 3 years after the issue date

if we assume: Current price: $0.25 Exercise price: $0.25 life: 3 years Risk free rate p.a: 0.2% volatility p.a: 85% The option cannot be exercised within the first 2 years, after 2 years, it is ...
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1 vote
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Option pricing under Vasicek, CIR, H-L and BDT model

I have implemented and calibrated recombining trees on Excel for the Vasicek, the Cox-Ingersoll-Ross, the Ho-Lee and the Black-Derman-Toy model. I now would like to price some options with these ...
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Strike Price Determination

Suppose you know the following: there are 2-month European call and put options on an index-like instrument with no dividends, the calculations show that the call option price is USD 10.1150, the spot ...
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1 answer
118 views

Maximum value of a call option proof [closed]

I'm reading Sinclair's Option Pricing and am confused by the proof for the maximum value of a call. It makes sense logically that a call can't be worth more than the underlying, and so: c <= S The ...
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Valuing Conditional "All Or Nothing" Multi Asset Options

I would like some insight as to how to value modified rainbow options on multiple assets: For example: A multi asset option, Call GOOG with $S_t$ \$1600 that you may exercise if and only if you also ...
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1 vote
1 answer
176 views

Why does the price of an option increase with increasing Rho?

I was wondering why the price of an option increases with Rho (price change for a derivative relative to a change in the risk-free rate of interest). I found this explanation on a website: "Each ...
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2 answers
171 views

Implementing a hedging strategy for oil future options

I am currently writing a paper examining two models for pricing options on WTI Crude oil futures, and I want to backtest hedging strategies from both model and compare them against each other. However,...
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2 votes
2 answers
177 views

Trading OTC FX options: choosing expiries

For FX options that are traded OTC vol quotes are given on a standardised grid, e.g. expiries 1D, 1W, 1M, 3M, 6M, etc. maturity and for each of these expiries you have quotes for ATM, 25 delta Risk ...
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How do you calculate optimal exercise boundary?

In the Broadie-Glasserman article there is a picture of simulated paths and Optimal Exercise region. How did they find this optimal exercise boudary?
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-1 votes
1 answer
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Buying an Option on Futures or entering a Futures contract

Let's say I want to hedge my current position using a futures or future options. What is the use of buying a future option if I can enter into the futures contract at zero cost(at any time before the ...
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Bachelier call option derivative w.r.t strike

I tried to take the partial derivative of the Bachelier call function w.r.t. strike price K (eqn 2.2 here), but my result is not lining up with what is shown on page 43 here.
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Hedging Options assuming a non-constant Yield Curve

I have read most of Shreve's Stochastic Calculus for Finance II. In it, the author prices various option types assuming an interest rate that is constant with respect to time. We can expand this model ...
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6 votes
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Options On Earthquakes

As a financial innovation, the options market is introducing Options contracts based on California Earthquakes. In your own words, discuss the following: True or False? “The sellers of Options on ...
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1 vote
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Calculating E^2[σ^2] where σ is a GARCH(1,1) Proces

Given that α =0,113079 β = 0,873884 ω = 0,0000081 Need the calculate a call price using garch volatility I alsa calculated the kurtosis = 235 enter image description here: https://www.researchgate.net/...
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3 answers
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List of Option Payoffs [closed]

Does anyone know of a good resource which lists all commonly used options together with their payoff functions? I'm specifically interested in non-path-dependent options.
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What free or cheap (<$200/month) API would you suggest to get stock options data?

Here is what I am looking for: I would like to cover the greatest possible percentage of all existing options worldwide (with US options being the top priority though). I would prefer live data but ...
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1 answer
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Sensitivity of correlation swaps to stochastic volatility

Are correlation swaps sensitive to stochastic volatility? Can you please justify from a theoretical point of view?
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Heston Nandi Garch Implementation Problem for Python

I have a coded my own Garch class in order to implement the Heston-Nandi Garch model. ...
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1 answer
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The most appropriate volatility model

Which would be the most appropriate models to find volatility trading opportunities (i.e. plot a theoretical volatility smile I can rely on) for the following instruments: Options on equity Options ...
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4 votes
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IR Cap Forward Premium

A well known broker quotes cap/floors as spot premium for ATM straddles but forward premium for the skew, given that the difference between spot premium and forward premium is that the option is not ...
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2 votes
1 answer
209 views

For what options does the "delta hedging rule" apply?

I'm reading Shreve's Stochastic Calculus for Finance, Volume II. In chapter 4, he derives the "delta hedging rule": $$\Delta(t) = c_x(t, S(t)) \text{ for all } t \in [0, T)\text{.}\tag{1}$$ ...
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4 votes
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Finding optimal calendar spreads and diagonals

I am looking for some pointers on risk/return profiles of calendar spreads and diagonals with different strikes and expiration dates, preferably based on historical backtests with SPY options. Please ...
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